4 � 4 4 � 2

4 � 1 4 � 12

Digital Resources

Launch

Find each quotient. Use a picture to represent each problem.

Reflect Which problem resulted in a quotient greater than 4? Why do you think that

happened?

Dividing Fractions and Whole Numbers

6-1

CCSS: 6.NS.A.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

MP1, MP4SAMPLE SOLUTIONS ARE SHOWN BELOW.

Sample: The problem 4 � 12 is equal to 8, so the quotient is

greater than 4. If you are dividing 4 by parts equal to 1, you will

get 4 parts. If you are dividing 4 by parts less than 1, then you

will get more than 4 parts.

0 1 2 3 4

4 ÷ 4 = 1 4 ÷ 2 = 2

0 1 2 3 4

4 ÷ 1 = 4

0 1 2 3 4 0 1 2 3 4

4 ÷ = 812

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Topic 6 133 Lesson 6-1

0 123

Got It?

When you divide a fraction by a whole number greater than one, how does the

quotient compare to the fraction? Explain your reasoning.

Part 1 Got It (2 of 2)

What division equation does this number line model show?

Part 1 Got It (1 of 2)

23 � 2 � 1

3

The quotient is less than the fraction. Dividing the fraction by a nonzero whole number is like dividing nonzero whole numbers. The quotient is less than the dividend.

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Topic 6 134 Lesson 6-1

0 321

Got It?

When you divide a nonzero whole number by a proper fraction, how does the

quotient compare to the whole number? Explain your reasoning.

A factory’s pipe-cutting machine cuts pieces of pipe to be threaded. The standard

length of pipe used for cutting is 8 feet. How many 23 ft long pieces of pipe can be

cut from a standard length of pipe?

Part 2 Got It (2 of 2)

What division equation does this number line model show?

Part 2 Got It (1 of 2)

Part 3 Got It

3 � 34 � 4

The quotient is greater than the whole number. Each equal segment is less than 1, so the number of equal segments is always greater than the number of whole number segments.

12

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Topic 6 135 Lesson 6-1

Close and Check

1. Use the number line to model 45 � 2.

Then write the solution.

0 1

2. Circle the division equation modeled by

the number line.

0 1 2 3 4

A. 3 �14

B. 12 �13

C. 4 �13

3. A fabric store donates 15 yards of

fabric for a community quilt project.

Each piece of fabric measures 58 yard.

How many 58-yard pieces of fabric is

the store donating?

4. Reasoning Will the quotient of a

proper fraction divided by a whole

number ever result in a whole

number? Explain.

5. Writing Explain why the first

expression can be rewritten as the

second expression.

5 �23 5 �

32

Focus QuestionHow does the relationship between multiplication and division help you to divide

fractions and whole numbers?

MP2, MP7

Sample: Multiplication and division have an inverse relationship.

Dividing is the same as multiplying by the reciprocal of the

divisor.

No. When a fraction is divided

by a whole number, the

quotient represents the value

of each lesser fractional part

of the original fraction.

Write 5 � 23 as 2

3

5 . Multiplying

by 32

32 results in a denominator

of 1. Then the numerators

can be multiplied. 5 � 3

2 5 � 32 5 � 3

223

5 23 � 3

21� � �

SAMPLE SOLUTIONS ARE SHOWN BELOW.

25

24

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Topic 6 136 Lesson 6-1